Heretofore, in the transfer or application of transfer films of decals to surfaces to be decorated, such films have usually been smoothed by hand with the aid of a squeegee or similar device to remove blisters or wrinkles and bubbles of air or of a solvent, such as water, which may exist or occur between said films and the surfaces to which such films are applied. The performance of such manual operations to smooth said transfer films and remove said bubbles etc. is relatively slow, difficult and uneconomical and, therefore, the apparatus of the present invention was developed to provide for faster and more economical decal smoothing, that is, automatic smoothing of the transfer films of the decals.